This paper investigates on an accurate channel estimation scheme for fast fading channels in multiple-input multiple-output (MIMO) mobile communications. A high-order exponential-weighted recursive least-squares (EW-RLS) method has been known as a good channel estimation scheme in rapid fading. however, there exists a drawback that we need to properly adjust the estimation order according to the channel environment. In this paper, we theoretically derive an optimum-weighted LS (OW-LS) channel estimation based on the statistical knowledge of the spatio-temporal channel correlation. Through the analysis, we reveal that the zero-th order polynomial becomes optimal when the optimum-weighting is employed. Furthermore, we propose an efficient recursive algorithm for channel tracking in oder to reduce the computational complexity. Since the proposed scheme automatically adapts the weighting coefficients to the channel condition, it has a significant advantage in mean-square error (MSE) performance compared to EW-RLS scheme.